Nov 14, 2012 4:00pm PST
based on feeding relationships between species; markets and economies linked together by the flow of capital. in some sense, we could argue that everything on the planet, both living and inanimate, is part of one huge, beautiful, but complicated network. what do all these networks have in common? abstractly, they are comprised of intersections, or points, that we call nodes, or vertices, that are connected by lines, or paths, that we call edges. now, on this map, for example, cities are nodes and highways are edges. any real-life network can look very messy. in order to get to the heart of a network, mathematicians strip away all the particulars, leaving only the essence, the underlying mathematical graph. it was just such a process of reducing a map to its basic components that laid the foundation for graph theory, network theory, and topology, three of the most bountiful areas of mathematics. and it all began with seven bridges when one of the greatest mathematicians of all time, leonhard euler, turned his attention to the famous puzzle of the konigsberg bridges in prussia in 1732.